7,557 research outputs found
Flat systems, equivalence and trajectory generation
Flat systems, an important subclass of nonlinear control systems introduced
via differential-algebraic methods, are defined in a differential
geometric framework. We utilize the infinite dimensional geometry developed
by Vinogradov and coworkers: a control system is a diffiety, or more
precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold
equipped with a privileged vector field. After recalling the definition of
a Lie-Backlund mapping, we say that two systems are equivalent if they
are related by a Lie-Backlund isomorphism. Flat systems are those systems
which are equivalent to a controllable linear one. The interest of
such an abstract setting relies mainly on the fact that the above system
equivalence is interpreted in terms of endogenous dynamic feedback. The
presentation is as elementary as possible and illustrated by the VTOL
aircraft
Fast algorithms for computing isogenies between elliptic curves
We survey algorithms for computing isogenies between elliptic curves defined
over a field of characteristic either 0 or a large prime. We introduce a new
algorithm that computes an isogeny of degree ( different from the
characteristic) in time quasi-linear with respect to . This is based in
particular on fast algorithms for power series expansion of the Weierstrass
-function and related functions
Sensitivity or Bayesian model updating: a comparison of techniques using the DLR AIRMOD test data
Deterministic model updating is now a mature technology widely applied to large-scale industrial structures. It is concerned with the calibration of the parameters of a single model based on one set of test data. It is, of course, well known that different analysts produce different finite element models, make different physics-based assumptions, and parameterize their models differently. Also, tests carried out on the same structure, by different operatives, at different times, under different ambient conditions produce different results. There is no unique model and no unique data. Therefore, model updating needs to take account of modeling and test-data variability. Much emphasis is now placed on what has become known as stochastic model updating where data are available from multiple nominally identical test structures. In this paper two currently prominent stochastic model updating techniques (sensitivity-based updating and Bayesian model updating) are described and applied to the DLR AIRMOD structure
Structural alphabets derived from attractors in conformational space
Background: The hierarchical and partially redundant nature of protein structures justifies the definition of frequently occurring conformations of short fragments as 'states'. Collections of selected representatives for these states define Structural Alphabets, describing the most typical local conformations within protein structures. These alphabets form a bridge between the string-oriented methods of sequence analysis and the coordinate-oriented methods of protein structure analysis.Results: A Structural Alphabet has been derived by clustering all four-residue fragments of a high-resolution subset of the protein data bank and extracting the high-density states as representative conformational states. Each fragment is uniquely defined by a set of three independent angles corresponding to its degrees of freedom, capturing in simple and intuitive terms the properties of the conformational space. The fragments of the Structural Alphabet are equivalent to the conformational attractors and therefore yield a most informative encoding of proteins. Proteins can be reconstructed within the experimental uncertainty in structure determination and ensembles of structures can be encoded with accuracy and robustness.Conclusions: The density-based Structural Alphabet provides a novel tool to describe local conformations and it is specifically suitable for application in studies of protein dynamics. © 2010 Pandini et al; licensee BioMed Central Ltd
Algebraic Topology
The chapter provides an introduction to the basic concepts of Algebraic
Topology with an emphasis on motivation from applications in the physical
sciences. It finishes with a brief review of computational work in algebraic
topology, including persistent homology.Comment: This manuscript will be published as Chapter 5 in Wiley's textbook
\emph{Mathematical Tools for Physicists}, 2nd edition, edited by Michael
Grinfeld from the University of Strathclyd
The elliptic dilogarithm for the sunset graph
We study the sunset graph defined as the scalar two-point self-energy at
two-loop order. We evaluate the sunset integral for all identical internal
masses in two dimensions. We give two calculations for the sunset amplitude;
one based on an interpretation of the amplitude as an inhomogeneous solution of
a classical Picard-Fuchs differential equation, and the other using arithmetic
algebraic geometry, motivic cohomology, and Eisenstein series. Both methods use
the rather special fact that the amplitude in this case is a family of periods
associated to the universal family of elliptic curves over the modular curve
X_1(6). We show that the integral is given by an elliptic dilogarithm evaluated
at a sixth root of unity modulo periods. We explain as well how this elliptic
dilogarithm value is related to the regulator of a class in the motivic
cohomology of the universal elliptic family.Comment: 3 figures, 43 pages. v2: minor corrections. version to be published
in The Journal of Number Theor
Gravitational Radiation Detection with Laser Interferometry
Gravitational-wave detection has been pursued relentlessly for over 40 years.
With the imminent operation of a new generation of laser interferometers, it is
expected that detections will become a common occurrence. The research into
more ambitious detectors promises to allow the field to move beyond detection
and into the realm of precision science using gravitational radiation. In this
article, I review the state of the art for the detectors and describe an
outlook for the coming decades.Comment: 38 pages typos, references update
- …